Solve the following Euler differential equations:
(a) $x^2 u^{\prime \prime}+5 x u^{\prime}-5 u=0$,
(b) $2 x^2 u^{\prime \prime}-x u^{\prime}-2 u=0$,
(c) $x^2 u^{\prime \prime}-u=0$,
(d) $x^2 u^{\prime \prime}+x u^{\prime}-3 u=0$,
(e) $3 x^2 u^{\prime \prime}-5 x u^{\prime}-3 u=0$,
(f) $\frac{d^2 u}{d x^2}+\frac{2}{x} \frac{d u}{d x}=0$.